DSC4825 Assignment 2 (660749) Exceptional Answers Due 1 July 2025

DSC4825
Assignment 02
(Exceptional Answers)
Due 1 July 2025

,DSC4825/2025

2 Compulsory Assignment 02
Unique number: 660749
Due date: 01 July 2025




Question 1 [8]
Thabo and Mashudu expect the stock price, currently at R50, to remain stable over 2
months. They buy one share and write at-the-money call options (strike price K = 50)
priced at R4.05. Thabo writes 2 calls, and Mashudu writes 4 calls.


1.1 [4]
To draw the profit and loss (P&L) diagram, we calculate the payoff at expiration for each
position and add the initial cash flows.

Thabo’s position: Long 1 share, short 2 calls. - Initial cash flow: Buy 1 share at R50,
cost = −50. Write 2 calls at R4.05 each, income = 2×4.05 = 8.10. Net cash flow = 8.10 − 50
= −41.90. - Payoff at expiration: - Share payoff = S T. - Each call payoff = −max(S T − 50,0).
For 2 calls, payoff = −2max(S T − 50,0). - Total payoff = S T − 2max(S T − 50,0). - Profit: Add
initial cash flow:

Profit = ST − 2max(ST − 50,0) − 41.90

- If ST ≤ 50: max(ST −50,0) = 0, profit = ST −41.90. - If ST > 50: max(ST − 50,0) = ST −50, profit
= ST −2(ST −50)−41.90 = S T −2ST +100−41.90 =

58.10 − ST.

Mashudu’s position: Long 1 share, short 4 calls. - Initial cash flow: Buy 1 share,
cost = −50. Write 4 calls, income = 4 × 4.05 = 16.20. Net cash flow = 16.20 − 50 = −33.80. -
Payoff at expiration: - Share payoff = ST. Four calls payoff = −4max(ST −50,0). - Total payoff
= ST −4max(ST −50,0).

- Profit:
Profit = ST − 4max(ST − 50,0) − 33.80

- If S T ≤ 50: Profit = S T −33.80. - If S T > 50: Profit = S T −4(ST −50)−33.80 = S T − 4S T + 200 −
33.80 = 166.20 − 3S T.



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, Diagram description: - Plot profit (y-axis) vs. stock price ST (x-axis). Thabo: Line with
slope 1 for S T ≤ 50, passing through (50,50−41.90 = 8.10). For S T> 50, slope −1, passing
through (50,8.10), e.g., at ST = 60, profit = 58.10−60 = −1.90. - Mashudu: Line with slope 1
for ST ≤ 50, passing through (50,50 − 33.80 = 16.20). For ST > 50, slope −3, passing through
(50,16.20), e.g., at S T = 60, profit = 166.20 − 3 × 60 = −13.80. - Both peak at S T= 50, with
Mashudu’s peak higher (16.20 vs. 8.10). Mashudu’s losses grow faster for S T > 50.


1.2 [2]
Their expectation is that the stock price will not move substantially, i.e., stay near R50.
Writing at-the-money calls generates premium income, which is maximized if the stock
price remains at or below R50 at expiration (calls expire worthless). Both strategies align
with this expectation, as they profit most when ST ≤ 50. The long share offsets losses if the
stock price rises slightly, but the strategy relies on limited price movement. Thus, both
strategies are consistent with their expectations.


1.3 [2]
If the stock price rises significantly (e.g., S T ≫ 50), both strategies incur losses, but
Mashudu’s are larger due to writing more calls: - Thabo’s profit = 58.10 − S T. At S T = 100,
profit = 58.10 − 100 = −41.90. - Mashudu’s profit = 166.20 − 3S
T. At ST = 100, profit = 166.20

− 300 = −133.80. Mashudu’s strategy is less appealing in a large upward movement
because losses increase three times faster than Thabo’s due to the higher number of short
calls. Thabo’s strategy is relatively safer in this scenario.




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